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# Last year Manfred received 26 paychecks. Each of his first 6

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Intern
Joined: 26 Feb 2011
Posts: 32
Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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Updated on: 02 Oct 2016, 21:02
3
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:29) correct 24% (01:35) wrong based on 215 sessions

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Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was$30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?

(A) $752 (B)$755
(C) $765 (D)$773
(E) $775 OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-manfred-received-26-paychecks-each-of-his-first-168484.html Originally posted by Madelaine88 on 03 Mar 2011, 06:16. Last edited by Bunuel on 02 Oct 2016, 21:02, edited 4 times in total. Renamed the topic and edited the question. Manager Joined: 14 Feb 2011 Posts: 175 Re: Last year Manfred received 26 paychecks. Each of his first 6 [#permalink] ### Show Tags 03 Mar 2011, 07:38 Madelaine88 wrote: Last year Manfred received 26 peychecks. Each of his first paychecks was$750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year? A/ 752 B/ 755 C/ 765 D/ 773 E/ 775 Are you sure about the numbers in the question? It doesn't seem right to me. Anyway, the approach would be as follows: One paycheck is 750 and remaining are 30 more, so 780 each. Hence, average should be (750 + 25*(750+30))/26 = 26*750/26 + 25*30/26 = 750 + ~29 = ~779. Intern Joined: 28 Jan 2011 Posts: 2 Re: Last year Manfred received 26 paychecks. Each of his first 6 [#permalink] ### Show Tags 03 Mar 2011, 10:31 Last year Manfred received 26 peychecks. Each of his first six paychecks was$750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year? first 6 paychecks was 750 = 6(750) = 4500 remaining paychecks (26-6 = 20) was 30 more = 20(750+30) = 15600 so 4500+15600/26 = 773 Intern Joined: 17 Nov 2008 Posts: 3 Re: Last year Manfred received 26 paychecks. Each of his first 6 [#permalink] ### Show Tags 25 Apr 2011, 03:42 Can the balancing method be used here? I am sure it can but not sure how....Can anyone help? thanks Retired Moderator Joined: 20 Dec 2010 Posts: 1810 Re: Last year Manfred received 26 paychecks. Each of his first 6 [#permalink] ### Show Tags 25 Apr 2011, 04:11 1 1 Madelaine88 wrote: Last year Manfred received 26 peychecks. Each of his first six paychecks was$750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year? A/ 752 B/ 755 C/ 765 D/ 773 E/ 775 R1: 750/check W1: 6 R2: 780/check W2: 20 R1-----W2----Avg------W1-----R2 750-----20----Avg------6-----780 20/6 = 10/3 750-----10----Avg------3-----780 780-750=30. (10/13)*30=300/13=23 Approx 750+23=773= Avg OR (3/13)*30=90/13=7 780-7=773=Avg Ans: "D" _________________ Director Joined: 01 Feb 2011 Posts: 658 Re: Last year Manfred received 26 paychecks. Each of his first 6 [#permalink] ### Show Tags 25 Apr 2011, 06:00 = (750*6+ 780 *20)/26 = 773 Answer is D. Posted from my mobile device Senior Manager Joined: 03 Mar 2010 Posts: 374 Schools: Simon '16 (M$)
Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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26 Apr 2011, 07:14
2
Last year Manfred received 26 peychecks. Each of his first six paychecks was $750; each of his remaining paychecks was$30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A/ 752
B/ 755
C/ 765
D/ 773
E/ 775

If M had received $750 for rest of the 20months as well, avg would have been$750. Since he received $30 more each month for 20months, total "extra" amount is$600.

$600 averaged over 26 paycheck = 600/26 ~ 23. Hence total avg: 750+23 = 773 OA. D _________________ My dad once said to me: Son, nothing succeeds like success. Manager Joined: 06 Feb 2011 Posts: 60 WE: Information Technology (Computer Software) Re: Last year Manfred received 26 paychecks. Each of his first 6 [#permalink] ### Show Tags 26 Apr 2011, 07:26 First 6 paychecks =$750, hence total is 750*6 = $4500 Next 20 paychecks =$780, hence total is 780*20 = $15600 Total =$20100. Hence monthly average = 20100/26 = 773
Manager
Joined: 09 Aug 2010
Posts: 91
Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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26 Apr 2011, 20:00
Last year Manfred received 26 peychecks. Each of his first six paychecks was $750; each of his remaining paychecks was$30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A/ 752
B/ 755
C/ 765
D/ 773
E/ 775

Total paychecks: p = 26

Round to 4/5 of 30 = $24.$750+$24 =$774. 20/26 slightly smaller than 4/5, so go with $773. Math Expert Joined: 02 Sep 2009 Posts: 52161 Re: Last year Manfred received 26 paychecks. Each of his first 6 [#permalink] ### Show Tags 02 Oct 2016, 21:03 Madelaine88 wrote: Last year Manfred received 26 paychecks. Each of his first 6 paychecks was$750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year? (A)$752
(B) $755 (C)$765
(D) $773 (E)$775

Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was$30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

(A) $752 (B)$755
(C) $765 (D)$773
(E) \$775

The average amount of the paychecks =

$$\frac{750*6+ (750 +30)*20}{26}=\frac{750*26+ 30*20}{26}=750+\frac{30*20}{26}=750+\frac{30*10}{13}\approx{750+23}=773$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-manfred-received-26-paychecks-each-of-his-first-168484.html
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Joined: 09 Sep 2013
Posts: 9415
Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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07 Jan 2019, 13:32
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Re: Last year Manfred received 26 paychecks. Each of his first 6 &nbs [#permalink] 07 Jan 2019, 13:32
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